Productively Fréchet spaces

Francis Jordan; Frédéric Mynard

Czechoslovak Mathematical Journal (2004)

  • Volume: 54, Issue: 4, page 981-990
  • ISSN: 0011-4642

Abstract

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We solve the long standing problem of characterizing the class of strongly Fréchet spaces whose product with every strongly Fréchet space is also Fréchet.

How to cite

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Jordan, Francis, and Mynard, Frédéric. "Productively Fréchet spaces." Czechoslovak Mathematical Journal 54.4 (2004): 981-990. <http://eudml.org/doc/30916>.

@article{Jordan2004,
abstract = {We solve the long standing problem of characterizing the class of strongly Fréchet spaces whose product with every strongly Fréchet space is also Fréchet.},
author = {Jordan, Francis, Mynard, Frédéric},
journal = {Czechoslovak Mathematical Journal},
keywords = {Fréchet; strongly Fréchet filters and spaces; product spaces; Fréchet; strongly Fréchet filters; strongly Fréchet spaces; product spaces},
language = {eng},
number = {4},
pages = {981-990},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Productively Fréchet spaces},
url = {http://eudml.org/doc/30916},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Jordan, Francis
AU - Mynard, Frédéric
TI - Productively Fréchet spaces
JO - Czechoslovak Mathematical Journal
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 4
SP - 981
EP - 990
AB - We solve the long standing problem of characterizing the class of strongly Fréchet spaces whose product with every strongly Fréchet space is also Fréchet.
LA - eng
KW - Fréchet; strongly Fréchet filters and spaces; product spaces; Fréchet; strongly Fréchet filters; strongly Fréchet spaces; product spaces
UR - http://eudml.org/doc/30916
ER -

References

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  1. The frequency spectrum of a topological space and the product operation, Trans. Moscow Math. Soc. 40 (1981), 163–200. (1981) 
  2. 10.1016/S0166-8641(00)90096-8, Topology Appl. 108 (2000), 43–52. (2000) MR1783423DOI10.1016/S0166-8641(00)90096-8
  3. 10.1016/0166-8641(96)00067-3, Topology Appl. 73 (1996), 1–21. (1996) MR1413721DOI10.1016/0166-8641(96)00067-3
  4. Active boundaries of upper semi-continuous and compactoid relations closed and inductively perfect maps, Rostock Math. Coll. 54 (2000), 51–68. (2000) MR1820118
  5. 10.1016/S0166-8641(99)00012-7, Topology Appl. 104 (2000), 67–99. (2000) MR1780899DOI10.1016/S0166-8641(99)00012-7
  6. 10.1023/A:1022420806729, Czechoslovak Math. J. 49 (1999), 421–429. (1999) MR1692508DOI10.1023/A:1022420806729
  7. 10.1016/0166-8641(92)90026-V, Topology Appl. 47 (1992), 163–164. (1992) Zbl0759.54013MR1192305DOI10.1016/0166-8641(92)90026-V
  8. On Fréchet spaces, Rend. Circ. Mat. Palermo (2) 18 (1988), 51–71. (1988) MR0958724
  9. A note on the product of Fréchet spaces, Topology Proc. 3 (1979), 109–115. (1979) Zbl0427.54017MR0540482
  10. 10.1002/mana.19750650109, Math. Nachr. 65 (1975), 117–123. (1975) DOI10.1002/mana.19750650109
  11. Compactoidness in topological spaces, (to appear). (to appear) 
  12. On countable spaces having no bicompactification of countable tightness, Dokl. Akad. Nauk SSR 206 (6) (1972), 1407–1411. (1972) Zbl0263.54015MR0320981
  13. 10.1016/0016-660X(72)90040-2, Gen. Topology Appl. 2 (1972), 91–138. (1972) Zbl0238.54009MR0309045DOI10.1016/0016-660X(72)90040-2
  14. Coreflectively modified continuous duality applied to classical product theorems, Applied Gen. Top. 2 (2001), 119–154. (2001) Zbl1007.54008MR1890032
  15. 10.1016/0166-8641(92)90021-Q, Topology Appl. 48 (1992), 91–116. (1992) MR1195504DOI10.1016/0166-8641(92)90021-Q
  16. Product of Fréchet spaces. General Topology and its relations to modern analysis and algebra VI, Proc. Prague Topological Sympos. 86 (1988), 371–378. (1988) MR0952623
  17. 10.1016/0166-8641(87)90076-9, Topology Appl. 25 (1987), 75–80. (1987) MR0874979DOI10.1016/0166-8641(87)90076-9
  18. 10.1023/A:1022829218525, Czechoslovak Math. J. 48 (1998), 207–227. (1998) MR1624303DOI10.1023/A:1022829218525
  19. 10.1023/A:1022877814524, Czechoslovak Math. J. 47 (1997), 337–340. (1997) DOI10.1023/A:1022877814524
  20. Concerning the topological product of two Fréchet spaces, General Topology and its relations to modern analysis and algebra IV, Proc. Fourth Prague Topological Sympos., 1977, pp. 342–343. (1977) MR0474222
  21. 10.1016/0016-660X(74)90002-6, Topology Appl. 4 (1974), 1–28. (1974) MR0365463DOI10.1016/0016-660X(74)90002-6
  22. A compact Fréchet space whose square is not Fréchet, Comment. Math. Univ. Carolin. 21 (1980), 749–753. (1980) Zbl0466.54022MR0597764
  23. 10.3792/pjaa.62.304, Proc. Japan Acad. Ser. A. Math. Sci. 62 (1986), 304–307. (1986) MR0868827DOI10.3792/pjaa.62.304
  24. Some applications of S and L combinatorics, Annals New York Acad. Sci., 1991, pp. 130–167. (1991) MR1277886

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